THE NATURE OF CHEMICAL STRUCTURE

We briefly discuss chemical structure as an object of mathematical characterization and list various structural invariants suitable for such a characterization. We restrict our attention to modeling compounds as graphs and examine several diverse structure-property-activity problems as an illustration of different mathematical analyses. Specifically, we consider: (1) the equivalence of an apparent quantum chemical problem as a graph theoretitcal decomposition (the analysis of diamagnetic susceptibility); (2) partial order as a tool for the illustration of regularities in isomeric variation of molecular properties (boiling points in alkanes); (3) ranking of structures as a tool in a search for biologically active substructures, illustrated on mutagenicity of nitrosamines; and (4) construction of search vectors as a tool for finding structures with a prescribed property. We end the discussion by pointing out advantages of mathematical descriptors versus physicochemical properties as descriptors. In conclusion, we focus attention on two problems facing graph theoretical approaches to chemical structure: How to incorporate differences between heteroatoms into molecular graphs, and how to incorporate spatial characteristics of chemical compounds into graph theoretical approaches. Finally, we generalize the traditional graph theoretical approaches, based on graphs and weighted graphs, to physicochemical matrices associated with molecular systems and point out the potential role that structural invariants play in discussions of molecular properties. Within this more general point of view, the quantum chemical computations produce but a fraction of the possible structural invariants that one may consider for a given system.